125
Views
0
CrossRef citations to date
0
Altmetric
Articles

Convex analysis of minimal time and signed minimal time functions

, , &
Pages 849-876 | Received 26 Oct 2020, Accepted 19 Mar 2021, Published online: 12 Apr 2021

References

  • Rubinov AM. Abstract convexity and global optimization. Dordreht (The Netherlands): Kluwer; 2000.
  • Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. 2nd ed. New York (NY): Springer; 2017.
  • Clarke FH. Nonsmooth analysis and optimization. New York (NY): Wiley; 1983.
  • Mordukhovich BS. Variational analysis and generalized differentiation, I: basic theory, II: applications. Berlin: Springer; 2006.
  • Mordukhovich BS. Variational analysis and applications. Cham (Switzerland): Springer; 2018.
  • Rockafellar RT, Wets RJ-B. Variational analysis. Berlin: Springer; 1998.
  • Altangerel L, Wanka G, Wilfer O. An oriented distance function application to gap functions for vector variational inequalities. In: Chinchuluun A, Pardalos PM, Enkhbat R, Pistikopoulos EN, editors. Optimization, simulation and control. New York (NY): Springer; 2013. p. 17–34.
  • Delfour MC, Zolesio JP. Shape analysis via oriented distance functions. J Funct Anal. 1994;123:129–201.
  • Hiriart-Urruty J-B. New concepts in nondifferentiable programming. Bull Soc Math France. 1979;60:5–85.
  • Khan AA, Tammer C, Zălinescu C. Set-Valued optimization: an introduction with applications. Berlin: Springer; 2015.
  • Luo H, Wang X, Lukens B. Variational analysis on the signed distance functions. J Optim Theory Appl. 2019;180:751–774.
  • Colombo G, Goncharov VV, Mordukhovich BS. Well-posedness of minimal time problem with constant dynamics in Banach spaces. Set-Valued Var Anal. 2010;18:349–372.
  • Colombo G, Wolenski PR. The subgradient formula for the minimal time function in the case of constant dynamics in Hilbert space. J Global Optim. 2004;28:269–282.
  • Colombo G, Wolenski PR. Variational analysis for a class of minimal time functions in Hilbert spaces. J Convex Anal. 2004;11:335–361.
  • Durea M, Huynh VN, Nguyen HT, et al. Metric regularity of composition set-valued mappings: metric setting and coderivative conditions. J Math Anal Appl. 2014;412:41–62.
  • Durea M, Paniruc M, Strugariu R. Minimal time function with respect to a set of directions: basic properties and applications. Optim Methods Softw. 2016;31:535–561.
  • Durea M, Paniruc M, Strugariu R. A new type of directional regularity for mappings and applications to optimization. SIAM J Optim. 2017;27:1204–1229.
  • He Y, Ng KF. Subdifferentials of a minimum time function in Banach spaces. J Math Anal Appl. 2006;321:896–910.
  • Mordukhovich BS, Nam NM. Limiting subgradients of minimal time functions in Banach spaces. J Global Optim. 2010;46:615–633.
  • Mordukhovich BS, Nam NM. Subgradients of minimal time functions under minimal requirements. J Convex Anal. 2011;18:915–947.
  • Mordukhovich BS, Nam NM. An easy path to convex analysis and applications. San Rafael (CA): Morgan & Claypool Publishers; 2014.
  • Nam NM, Cuong DV. Subgradients of minimal time functions without calmness. J Convex Anal. 2019;26:189–200.
  • Nam NM, Villalobos MC, An NT. Minimal time functions and the smallest intersecting ball problem with unbounded dynamics. J Optim Theory Appl. 2012;154:768–791.
  • Nam NM, Zălinescu C. Variational analysis of directional minimal time functions and applications to location problems. Set-Valued Var Anal. 2013;21:405–430.
  • Zălinescu C. Convex analysis in general vector spaces. Singapore: World Scientific; 2002.
  • Meise R, Vogt D. Introduction to functional analysis. Oxford: Oxford University Press; 1997.
  • Borwein JM, Vanderwerff JD. Convex functions: constructions, characterizations and counterexamples. Cambridge: Cambridge University Press; 2010.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.